𝐓𝐡𝐞 𝐑𝐨𝐨𝐭𝐬 𝐨𝐟 𝐔𝐧𝐢𝐭𝐲
A degree 𝑛 polynomial has 𝑛 complex roots
The cube root of 1 is not just 1, but also has 2 other "cube roots of unity"pic.twitter.com/jR4cHjTRLl
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Multiplication by eⁱˣ is just a rotation along the unit circle in the complex plane
The cube roots of unity are therefore 3 distinct rotations that result in 1, after 3 successive applications.
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So Unity = one Real world plus two facets of an Imaginary world We learnt that much in high school
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Don't you have some homework to do or something ? Oh wait, I know. You are playing at the computer with your left brain while your right brain finds the general solution to the classical Yang-Mills field equations.
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Lmao no, no homework.. just research.. but i do things that i find fun first so I don’t lose the passion and fun that got me so far in the first place
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A "U(1) ~ SO(2)" rotation: z'=z*e^(ia)=x'+iy'= (x+iy)(cos(a)+i sin(a)), yielding: z'^2=z^2 or r'^2=x'^2+y'^2=x^2+y^2=r^2 where: x'= x cos a - y sin a y'= x sin a + y cos a and r=1 in case of a unit circle ;-)
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